Table 7. Performance across variations in measurement error.
Type of error | Model specification | Method | MAD | NOTFront | PU20% | PO20% | rs |
---|---|---|---|---|---|---|---|
Additive measurement error | θi ∼ unif(0,1), vi ∼ N(0, 0.022) | DEA | 0.069 | 11.8% | 0.1% | 44.2% | 0.862 |
rDEA | 0.022 | 2.7% | 0.2% | 9.8% | 0.963 | ||
rSDF-CD | 0.095 | 0.0% | 32.2% | 26.4% | 0.797 | ||
ENS | 0.048 | 0.0% | 9.6% | 20.6% | 0.940 | ||
θi ∼ unif(0,1), vi ∼ N(0, 0.082) | DEA | 0.072 | 12.0% | 0.8% | 45.7% | 0.851 | |
rDEA | 0.028 | 2.8% | 1.8% | 15.3% | 0.953 | ||
rSDF-CD | 0.102 | 0.0% | 35.0% | 25.5% | 0.779 | ||
ENS | 0.054 | 0.0% | 13.8% | 21.1% | 0.929 | ||
Multiplicative measurement error | θi ∼ unif(0,1), vi ∼ N(0, 0.022) | DEA | 0.068 | 11.8% | 0.0% | 42.6% | 0.862 |
rDEA | 0.026 | 2.7% | 2.0% | 7.4% | 0.953 | ||
rSDF-CD | 0.106 | 0.0% | 50.3% | 10.5% | 0.762 | ||
ENS | 0.056 | 0.0% | 26.5% | 6.3% | 0.935 | ||
θi ∼ unif(0,1), vi ∼ N(0, 0.082) | DEA | 0.071 | 11.9% | 0.4% | 42.7% | 0.847 | |
rDEA | 0.043 | 2.8% | 12.4% | 9.3% | 0.936 | ||
rSDF-CD | 0.109 | 0.0% | 51.1% | 10.9% | 0.759 | ||
ENS | 0.066 | 0.0% | 34.1% | 6.5% | 0.926 | ||
Mixed measurement error | θi ∼ unif(0,1) | DEA | 0.068 | 11.8% | 0.0% | 42.7% | 0.859 |
rDEA | 0.030 | 2.8% | 3.3% | 8.0% | 0.950 | ||
rSDF-CD | 0.107 | 0.0% | 50.4% | 10.6% | 0.762 | ||
ENS | 0.058 | 0.0% | 28.1% | 6.3% | 0.933 |
Note: Numbers in bold highlight the best outcome for each performance indicator across the alternative approaches. MAD: median absolute deviation, NOTFront: percentage of misclassified DMUs, PU20%: percentage of underestimation, PO20%: percentage of overestimation, rs: Spearman’s rank correlation.